Basic properties
Modulus: | \(3724\) | |
Conductor: | \(3724\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(126\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3724.ei
\(\chi_{3724}(43,\cdot)\) \(\chi_{3724}(351,\cdot)\) \(\chi_{3724}(435,\cdot)\) \(\chi_{3724}(519,\cdot)\) \(\chi_{3724}(575,\cdot)\) \(\chi_{3724}(631,\cdot)\) \(\chi_{3724}(967,\cdot)\) \(\chi_{3724}(1023,\cdot)\) \(\chi_{3724}(1051,\cdot)\) \(\chi_{3724}(1107,\cdot)\) \(\chi_{3724}(1163,\cdot)\) \(\chi_{3724}(1415,\cdot)\) \(\chi_{3724}(1499,\cdot)\) \(\chi_{3724}(1555,\cdot)\) \(\chi_{3724}(1583,\cdot)\) \(\chi_{3724}(1639,\cdot)\) \(\chi_{3724}(1695,\cdot)\) \(\chi_{3724}(1947,\cdot)\) \(\chi_{3724}(2031,\cdot)\) \(\chi_{3724}(2087,\cdot)\) \(\chi_{3724}(2115,\cdot)\) \(\chi_{3724}(2171,\cdot)\) \(\chi_{3724}(2227,\cdot)\) \(\chi_{3724}(2479,\cdot)\) \(\chi_{3724}(2563,\cdot)\) \(\chi_{3724}(2619,\cdot)\) \(\chi_{3724}(2703,\cdot)\) \(\chi_{3724}(2759,\cdot)\) \(\chi_{3724}(3011,\cdot)\) \(\chi_{3724}(3095,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{63})$ |
Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((1863,3041,3137)\) → \((-1,e\left(\frac{5}{7}\right),e\left(\frac{8}{9}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(23\) | \(25\) | \(27\) |
\( \chi_{ 3724 }(2171, a) \) | \(-1\) | \(1\) | \(e\left(\frac{97}{126}\right)\) | \(e\left(\frac{59}{63}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{31}{42}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{89}{126}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{53}{126}\right)\) | \(e\left(\frac{55}{63}\right)\) | \(e\left(\frac{13}{42}\right)\) |